Archive for tag:
Borda

A recent project brought to mind a simple approach to ranking
alternatives for facility decision makers.

To prioritize facility investments, the U.S. Coast Guard needed
to rank its various missions. The approach it adopted was the
Analytical Hierarchy Process (AHP), a well-known decision analysis
method. [1] There were eight missions and the rankings were to be
determined by a panel of senior officers. Using a web-based survey,
each officer was asked to rate the importance of each mission to
the other missions, so that 28 pair wise comparisons were required.
The survey took an estimated 60 minutes to complete for each
officer. The comparisons were combined into a matrix of paired
comparisons and then, with a specialized software product,
mathematically reduced to a preference score or ranking that ranged
from 0 to 100. [2] The results were reasonable, but the process
seemed overwrought-particularly if it was to be repeated
annually.

An alternative approach would be to skip the arduous pair-wise
comparison, and simply ask each officer to assign a rank to each
mission, then sum the ranks, and sort from highest to lowest
value. Known as the Borda Count Method, this is often used in
polls and elections-as examples, a modified version is used to
score competitive sailing regattas and to rank Heisman Trophy
candidates. How do the results differ between the two
approaches? Not much it seems. We approximated Borda
scores using the survey responses of the individual officers and
compared the results:

_

AHP

_

Borda

_

Mission

Score

Rank

Score

Rank

A

100

1

100

1

B

77

2

89

2

C

42

4

60

4

D

46

3

80

3

E

33

5

59

5

F

26

6

58

6

G

13

7

22

8

H

13

8

30

7

The standardized scores differed substantially, but the mission
rankings were almost the same, with a reversal of 7th
and 8th place. In other words, the Borda Method led to
similar results for a lot less effort. Analysts with a critical
bent could debate the merits of other approaches, but for those
looking for a quick and transparent way to rank and prioritize (and
for those whose matrix algebra is a little hazy) the Borda approach
is worth a look. [3]

Postscript: We learned yesterday the Coast Guard has indeed
switched to the Borda Count Method.

[2] The scores are the eigenvector of the matrix of pairwise
comparisons.

[3] For a detailed discussion of alternative voting methods, see
Donald G. Saari, Explaining all three-alternative outcomes.
Journal of Economic Theory 87, 1999; or see a summary of
Saari's article at http://www.economist.com/node/288778 .